1. Fundamentals of IT UNIT-I OnlyforIPMCA

2. DIGITAL SIGNALS & LOGIC GATES Signals and data are classified as analog or digital. Analog refers to something that is continuous- a set of data and all possible points between. An example of analog data is the human voice. Digital refers to something that is discrete –a set of specific points of data with no other points in between. An example of digital data is data stored in the memory of a computer in the form of 0s and 1s. OnlyforIPMCA

3. Contd.. An analog signal is a continuous wave form that changes smoothly. As the wave moves from a value A to a value B, it passes through and includes an infinite number of values along its path. A digital signal can have only a limited number of defined values, often as simple as 1 and 0. OnlyforIPMCA

5. Comparison of analog and digital signals Signals can be analog or digital. Analog signals can have an infinite number of values in a range; digital signals can have only a limited number of values. OnlyforIPMCA

6. LOGIC GATES Logic diagram: a graphical representation of a circuit – Each type of gate is represented by a specific graphical symbol Truth table: defines the function of a gate by listing all possible input combinations that the gate could encounter, and the corresponding output OnlyforIPMCA

7. Let’s examine the processing of the following six types of gates – NOT – AND – OR – XOR – NAND – NOR Typically, logic diagrams are black and white, and the gates are distinguished only by their shape OnlyforIPMCA

8. NOT GATE A NOT gate accepts one input value and produces one output value OnlyforIPMCA

9. AND GATE An AND gate accepts two input signals If the two input values for an AND gate are both 1, the output is 1; otherwise, the output is 0 OnlyforIPMCA

10. OR GATE If the two input values are both 0, the output value is 0; otherwise, the output is 1 OnlyforIPMCA

11. XOR GATE XOR, or exclusive OR, gate – An XOR gate produces 0 if its two inputs are the same, and a 1 otherwise When both input signals are 1, the OR gate produces a 1 and the XOR produces a 0 OnlyforIPMCA

12. NAND & NOR The NAND and NOR gates are essentially the opposite of the AND and OR gates, respectively OnlyforIPMCA

13. Number Systems SystemBaseSymbols Used by humans? Used in computers? Decimal100, 1, … 9YesNo Binary20, 1NoYes Octal80, 1, … 7No Hexa- decimal 160, 1, … 9, A, B, … F No OnlyforIPMCA

14. Quantities/Counting (1 of 3) DecimalBinaryOctal Hexa- decimal 0000 1111 21022 31133 410044 510155 611066 711177 OnlyforIPMCA

15. Quantities/Counting (2 of 3) DecimalBinaryOctal Hexa- decimal 81000108 91001119 10101012A 11101113B 12110014C 13110115D 14111016E 15111117F OnlyforIPMCA

16. Quantities/Counting (3 of 3) DecimalBinaryOctal Hexa- decimal 16100002010 17100012111 18100102212 19100112313 20101002414 21101012515 22101102616 23101112717 Etc. OnlyforIPMCA

17. Conversion Among Bases The possibilities: Hexadecimal DecimalOctal Binary OnlyforIPMCA

18. Decimal to Decimal (just for fun) Hexadecimal DecimalOctal Binary OnlyforIPMCA

19. 125 10 =>5 x 10 0 = 5 2 x 10 1 = 20 1 x 10 2 = 100 125 Base Weight OnlyforIPMCA

20. Binary to Decimal Hexadecimal DecimalOctal Binary OnlyforIPMCA

21. Binary to Decimal Technique – Multiply each bit by 2 n, where n is the “weight” of the bit – The weight is the position of the bit, starting from 0 on the right – Add the results OnlyforIPMCA

22. Example 101011 2 => 1 x 2 0 = 1 1 x 2 1 = 2 0 x 2 2 = 0 1 x 2 3 = 8 0 x 2 4 = 0 1 x 2 5 = 32 43 10 Bit “0” OnlyforIPMCA

23. Octal to Decimal Hexadecimal DecimalOctal Binary OnlyforIPMCA

24. Octal to Decimal Technique – Multiply each bit by 8 n, where n is the “weight” of the bit – The weight is the position of the bit, starting from 0 on the right – Add the results OnlyforIPMCA

25. Example 724 8 => 4 x 8 0 = 4 2 x 8 1 = 16 7 x 8 2 = 448 468 10 OnlyforIPMCA

26. Hexadecimal to Decimal Hexadecimal DecimalOctal Binary OnlyforIPMCA

27. Hexadecimal to Decimal Technique – Multiply each bit by 16 n, where n is the “weight” of the bit – The weight is the position of the bit, starting from 0 on the right – Add the results OnlyforIPMCA

28. Example ABC 16 =>C x 16 0 = 12 x 1 = 12 B x 16 1 = 11 x 16 = 176 A x 16 2 = 10 x 256 = 2560 2748 10 OnlyforIPMCA

29. Decimal to Binary Hexadecimal DecimalOctal Binary OnlyforIPMCA

30. Decimal to Binary Technique – Divide by two, keep track of the remainder – First remainder is bit 0 (LSB, least-significant bit) – Second remainder is bit 1 – Etc. OnlyforIPMCA

31. Example 125 10 = ? 2 2 125 62 1 2 31 0 2 15 1 2 7 1 2 3 1 2 1 1 2 0 1 125 10 = 1111101 2 OnlyforIPMCA

32. Decimal to Octal Hexadecimal DecimalOctal Binary OnlyforIPMCA

33. Decimal to Octal Technique – Divide by 8 – Keep track of the remainder OnlyforIPMCA

34. Example 1234 10 = ? 8 8 1234 154 2 8 19 2 8 2 3 8 0 2 1234 10 = 2322 8 OnlyforIPMCA

35. Decimal to Hexadecimal Hexadecimal DecimalOctal Binary OnlyforIPMCA

36. Decimal to Hexadecimal Technique – Divide by 16 – Keep track of the remainder OnlyforIPMCA

37. Example 1234 10 = ? 16 1234 10 = 4D2 16 16 1234 77 2 16 4 13 = D 16 0 4 OnlyforIPMCA

38. Octal to Binary Hexadecimal DecimalOctal Binary OnlyforIPMCA

39. Octal to Binary Technique – Convert each octal digit to a 3-bit equivalent binary representation OnlyforIPMCA

40. Example 705 8 = ? 2 7 0 5 111 000 101 705 8 = 111000101 2 OnlyforIPMCA

41. Hexadecimal to Binary Hexadecimal DecimalOctal Binary OnlyforIPMCA

42. Hexadecimal to Binary Technique – Convert each hexadecimal digit to a 4-bit equivalent binary representation OnlyforIPMCA

43. Example 10AF 16 = ? 2 1 0 A F 0001 0000 1010 1111 10AF 16 = 0001000010101111 2 OnlyforIPMCA

44. Binary to Octal Hexadecimal DecimalOctal Binary OnlyforIPMCA

45. Binary to Octal Technique – Group bits in threes, starting on right – Convert to octal digits OnlyforIPMCA

46. Example 1011010111 2 = ? 8 1 011 010 111 1 3 2 7 1011010111 2 = 1327 8 OnlyforIPMCA

47. Binary to Hexadecimal Hexadecimal DecimalOctal Binary OnlyforIPMCA

48. Binary to Hexadecimal Technique – Group bits in fours, starting on right – Convert to hexadecimal digits OnlyforIPMCA

49. Example 1010111011 2 = ? 16 10 1011 1011 2 B B 1010111011 2 = 2BB 16 OnlyforIPMCA

50. Octal to Hexadecimal Hexadecimal DecimalOctal Binary OnlyforIPMCA

51. Octal to Hexadecimal Technique – Use binary as an intermediary OnlyforIPMCA

52. Example 1076 8 = ? 16 1 0 7 6 001 000 111 110 2 3 E 1076 8 = 23E 16 OnlyforIPMCA

53. Hexadecimal to Octal Hexadecimal DecimalOctal Binary OnlyforIPMCA

54. Hexadecimal to Octal Technique – Use binary as an intermediary OnlyforIPMCA

55. Example 1F0C 16 = ? 8 1 F 0 C 0001 1111 0000 1100 1 7 4 1 4 1F0C 16 = 17414 8 OnlyforIPMCA

56. Exercise – Convert... Don’t use a calculator! DecimalBinaryOctal Hexa- decimal 33 1110101 703 1AF Skip answer Answer OnlyforIPMCA

57. Exercise – Convert … DecimalBinaryOctal Hexa- decimal 331000014121 117111010116575 4511110000117031C3 4311101011116571AF Answer OnlyforIPMCA

58. Binary Addition (1 of 2) Two 1-bit values ABA + B 000 011 101 1110 “two” OnlyforIPMCA

59. Binary Addition (2 of 2) Two n-bit values – Add individual bits – Propagate carries – E.g., 10101 21 + 11001 + 25 101110 46 11 OnlyforIPMCA

60. Multiplication (1 of 3) Decimal (just for fun) 35 x 105 175 000 35 3675 OnlyforIPMCA

61. Binary Multiplication AB A  B 000 010 100 111 OnlyforIPMCA

62. Multiplication Binary, two n-bit values – As with decimal values – E.g., 1110 x 1011 1110 1110 0000 1110 10011010 OnlyforIPMCA

63. Fractions Decimal to decimal (just for fun) 3.14 =>4 x 10 -2 = 0.04 1 x 10 -1 = 0.1 3 x 10 0 = 3 3.14 OnlyforIPMCA

64. Fractions Fractions - Binary to decimal 10.1011 => 1 x 2 -4 = 0.0625 1 x 2 -3 = 0.125 0 x 2 -2 = 0.0 1 x 2 -1 = 0.5 0 x 2 0 = 0.0 1 x 2 1 = 2.0 2.6875 OnlyforIPMCA

65. Fractions Decimal to binary 3.14579.14579 x 2 0.29158 x 2 0.58316 x 2 1.16632 x 2 0.33264 x 2 0.66528 x 2 1.33056 etc. 11.001001... OnlyforIPMCA

66. Exercise – Convert... Don’t use a calculator! DecimalBinaryOctal Hexa- decimal 29.8 101.1101 3.07 C.82 OnlyforIPMCA

67. Exercise – Convert … DecimalBinaryOctal Hexa- decimal 29.811101.110011…35.63…1D.CC… 5.8125101.11015.645.D 3.10937511.0001113.073.1C 12.50781251100.1000001014.404C.82 Answer OnlyforIPMCA